A new process has been designed to make ceramic tiles. The goal is to have no more than 5% of the tiles be nonconforming due to surface defects. A random sample of 1000 tiles is inspected. Let p̂ be the proportion of nonconforming tiles in the sample.

a. If 5% of the tiles produced are nonconforming, what is P(p̂ ≥ 0.075)?

b. Based on the answer to part (a), if 5% of the tiles are nonconforming, is a proportion of 0.075 nonconforming tiles in a sample of 1000 unusually large?

c. If the sample proportion of nonconforming tiles were 0.075, would it be plausible that the goal had been reached?

Explain.

d. If 5% of the tiles produced are nonconforming, what is P(p̂ ≥ 0.053)?

e. Based on the answer to part (d), if 5% of the tiles are nonconforming, is a proportion of 0.053 nonconforming tiles in a sample of 1000 unusually large?

f. If the sample proportion of nonconforming tiles were 0.053, would it be plausible that the goal had been reached?

Explain.